A Transition to Proof
An Introduction to Advanced Mathematics
Seiten
2023
CRC Press (Verlag)
978-1-032-47572-1 (ISBN)
CRC Press (Verlag)
978-1-032-47572-1 (ISBN)
The fundamental tool of theoretical mathematics is mathematical proof. Any claim or justification a mathematician makes must be proven. This book is designed for a reader who wants to learn what exactly a mathematical proof is, how they are constructed, and how to go about writing one.
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively.
The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof.
Features:
The text is aimed at transition courses preparing students to take analysis
Promotes creativity, intuition, and accuracy in exposition
The language of proof is established in the first two chapters, which cover logic and set theory
Includes chapters on cardinality and introductory topology
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively.
The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof.
Features:
The text is aimed at transition courses preparing students to take analysis
Promotes creativity, intuition, and accuracy in exposition
The language of proof is established in the first two chapters, which cover logic and set theory
Includes chapters on cardinality and introductory topology
Dr. Neil R. Nicholson is Associate Professor of Mathematics at North Central College. He holds a Ph.D. in Mathematics from The University of Iowa, specializing in knot theory. His research interests have consistently been topics accessible to undergraduates; collaborating with them on original research is a fundamental goal of his professional development. In 2015, he earned the Clarence F. Dissinger Award for Junior Faculty Teaching at North Central College. He serves as the Faculty Athletic Representative to the NCAA for North Central College.
Symbolic Logic
Sets
Introduction to Proofs
Mathematical Induction
Relations
Functions
Cardinality
Introduction to Topology
Properties of the Real Number System
Proof Writing Tips
Selected Solutions and Hints
| Erscheinungsdatum | 11.01.2023 |
|---|---|
| Reihe/Serie | Textbooks in Mathematics |
| Zusatzinfo | 39 Illustrations, black and white |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 453 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-032-47572-2 / 1032475722 |
| ISBN-13 | 978-1-032-47572-1 / 9781032475721 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
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